ETD question re: unisons

[Richard Brekne]

Grin... I love it Clark... These articles easy to pick up ??? or do I have
to pay JASA for them ?

Thanks for the very informative reply... got some more reading material I
see....num num...

Clark wrote:

> Richard Brekne wrote:
>
> > I am curious.... just how many of you have read Gabriel Weinreichs
> > paper "The coupled motion of piano strings" ?
>
> This seems to be three papers, due editing - the JASA version being the
> most technical (JASA v.62 nr.6 [Dec. '77] - p.1474-1484), and the SciAm
> apparently the least scientific. The phenomenon of coupling he describes
> also has been applied to single strings (Sankey) and to account for the
> presence of theoretically missing partials (Legge and Fletcher).
>
> The latter ("Nonlinear generation of missing modes on a vibrating
> string". JASA v.76 nr.1 [Jul. '84] - p.5-12) might account for Ron's
> observation of backscale influence to pitch drop. Their model uses
> bridge compliance to explain a partial failure of Young's law, where
> partials corresponding to striking points are predicted to be absent
> (C.V. Raman observes its complete failure for vina and tanpura due their
> unique bridges). Legge and Fletcher predict the coupling magnitude for
> the indirectly generated missing partial (of a single string) will be
> proportional to the backscale length and its bearing height at the
> bridge (they write [sin(w)], where [w] is the bearing angle), and
> behaves as the square of the initial amplitude, arising somewhat later
> than the characteristic partials.
>
> The mechanical properties of the bridge assembly (not always uniform
> even within a unison!) may be modified by the strings themselves - by
> speaking lengths, bearing, number of strings in motion and backscale
> lengths. It should be that the behavior of multiple strings will differ
> from that of a single - the basis for Weinreich's theories - and
> obviously backscales can be classed as coupled vibrating strings.
>
> Clark

--
Richard Brekne
RPT, N.P.T.F.
Bergen, Norway
mailto:Richard.Brekne@grieg.uib.no